Triangle Classification: Is This an Acute-Angled Triangle?

Q: How can I tell if an angle is acute just by looking?

Look for sharp, pointed corners. Acute angles appear "pointy" - less open than a square corner. If all three corners look sharp and none appear to form a square corner or be wider, it's likely acute.

Q: What's the difference between acute, right, and obtuse triangles?

Acute: All angles $90^\circ$ (all sharp)Right: One angle = $90^\circ$ (square corner)Obtuse: One angle > $90^\circ$ (wide, open angle)

Q: Can a triangle have more than one obtuse angle?

No! A triangle can have at most one obtuse angle. Since all angles must add up to $180^\circ$, having two obtuse angles (each > $90^\circ$) would exceed this total.

Q: Why does the triangle in the drawing look so tall?

Triangle shape doesn't determine angle type. A triangle can be tall, wide, or any shape and still be acute. Focus on the angles at each vertex, not the overall proportions.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine whether the triangle is acute-angled

00:03 Proceed to examine all the angles

00:06 All of them are less than 90 degrees, therefore the triangle is acute-angled, and that's the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Is the triangle in the drawing an acute-angled triangle?

2

Step-by-step solution

To solve this problem, we'll analyze the key features of an acute-angled triangle and determine if the triangle in the drawing fits this classification.

Definition Review: An acute-angled triangle is a triangle where all interior angles are less than $90^\circ$ . This implies examining the geometric structure to ensure no angles exceed or equal $90^\circ$ .

Steps for Verification:

Analyze whether changes in angles can lead to right or obtuse angles.
Check features such as side length variations that help confirm this in various geometries.
Consider symmetry or specific style if indicated in a complete or symmetrical manner supporting acute settings.

Conclusion:
Upon analysis of these guiding factors and geometric principles relevant to acute-angled triangles, and considering configurations leading to all sharp interior angles, we conclude: Yes, the triangle is acute-angled.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic

Definition: Acute triangles have all three angles less than $90^\circ$
Visual Check: Look for sharp corners - no right angles or wide obtuse angles
Verification: All three vertices appear sharp and pointed, confirming acute classification ✓

Common Mistakes

Avoid these frequent errors

Confusing angle types based on triangle appearance
Don't assume a tall or wide triangle is automatically obtuse or right-angled = wrong classification! Triangle shape alone doesn't determine angle types. Always examine each individual angle carefully to see if any appear to be 90° or greater.

Practice Quiz

Test your knowledge with interactive questions

In a right triangle, the side opposite the right angle is called....?

FAQ

Everything you need to know about this question

How can I tell if an angle is acute just by looking?

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Look for sharp, pointed corners. Acute angles appear "pointy" - less open than a square corner. If all three corners look sharp and none appear to form a square corner or be wider, it's likely acute.

What's the difference between acute, right, and obtuse triangles?

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Acute: All angles < $90^\circ$ (all sharp)
Right: One angle = $90^\circ$ (square corner)
Obtuse: One angle > $90^\circ$ (wide, open angle)

Can a triangle have more than one obtuse angle?

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No! A triangle can have at most one obtuse angle. Since all angles must add up to $180^\circ$ , having two obtuse angles (each > $90^\circ$ ) would exceed this total.

Do I need to measure the angles to be sure?

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For this visual problem, careful observation is sufficient. Look for obvious right angles (square corners) or very wide angles. If all corners appear sharp and pointed, the triangle is acute.

Why does the triangle in the drawing look so tall?

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Triangle shape doesn't determine angle type. A triangle can be tall, wide, or any shape and still be acute. Focus on the angles at each vertex, not the overall proportions.

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Triangle Classification: Is This an Acute-Angled Triangle?

Triangle Classification with Angle Analysis

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